Table of Contents

Introduction.; 1. The large sieve inequality; 2. An extension of the classical arithmetical theory of the large sieve.; 3. Some general remarks on arithmetical functions; 4. A Geometric interpretation; 5. Further arithmetical applications; 6. The Siegel zero effect; 7. A weighted hermitian inequality; 8. A first use of local models; 9. Twin primes and local models; 10. The three primes theorem; 11. The Selberg sieve; 12. Fourier expansion of sieve weights; 13. The Selberg sieve for sequences; 14. An overview; 15. Some weighted sequences; 16. Small gaps between primes; 17. Approximating by a local model; 18. Selecting other sets of moduli; 19. Sums of two squarefree numbers; 20. On large sieve equality.; Appendix. Notations. References. Index.